A111305 -id:A111305 - cp's OEIS frontend

A209211 Numbers n such that n-1 and phi(n) are relatively prime.

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 54, 56, 58, 60, 62, 64, 68, 72, 74, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 114, 116, 118, 120, 122, 126, 128, 132, 134, 136, 138

Offset: 1

José María Grau Ribas, Mar 06 2012

nonn

A063994(a(n)) = 1. - Reinhard Zumkeller, Mar 02 2013
a(n) = A111305(n-2) for n >= 3. - Emmanuel Vantieghem, Jul 03 2013
n such that A049559(n) = 1.  Includes A100484 and A000079. - Robert Israel, Nov 09 2015
All terms except the first one are even. Missing even terms are A039772. - Robert G. Wilson v, Sep 26 2016
Numbers n such that A187730(n) = 1. - Thomas Ordowski, Dec 29 2016

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000010, A000079, A003277, A039772, A049559, A063994, A100484, A111305.

a209211 n = a209211_list !! (n-1)
a209211_list = filter (\x -> (x - 1) `gcd` a000010 x == 1) [1..]
-- Reinhard Zumkeller, Mar 02 2013

select(n -> igcd(n-1, numtheory:-phi(n)) = 1, [$1..1000]); # Robert Israel, Nov 09 2015

Select[Range[200], GCD[# - 1, EulerPhi[#]] == 1 &]

isok(n) = gcd(n-1, eulerphi(n)) == 1; \\ Michel Marcus, Sep 26 2016

A227180 Composite numbers n such that b^(n-1) == 1 (mod n) implies b == -1 or +1 (mod n).

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 54, 56, 58, 60, 62, 64, 68, 72, 74, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 114, 116, 118, 120, 122, 126, 128, 132, 134, 136, 138, 140, 142, 144, 146, 150, 152, 156, 158, 160, 162, 164, 166, 168, 170

Offset: 1

Emmanuel Vantieghem, Jul 03 2013

nonn

The sequence is the union of A111305 with {3^k | k > 1}.

The composite numbers not in this sequence are the Fermat pseudoprimes A181780.

Cf. A111305, A181780, A209211.

FQ[k_]:= Block[{},GCD[EulerPhi[k],k-1]==1||IntegerQ[Log[3,k]]];Select[Range[4,170],FQ]

is(n)=for(b=2, n-2, if(Mod(b, n)^(n-1)==1, return(0))); !isprime(n) \\ Charles R Greathouse IV, Dec 22 2016

cp's OEIS Frontend

A209211 Numbers n such that n-1 and phi(n) are relatively prime.

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